(2016 Exam) One of the major high street banks has a branch in a large university town. In the current
economic climate, the bank has found that it faces considerable demand for its finance from students
(who wish to use the money borrowed for a variety of purposes). The loan budget for the next accounting
period has been set by the bank's head office at 1.5 million. The branch currently categorizes three types
of student loan: a general-purpose loan which may be either secured or unsecured and a loan for the
purpose of purchasing a car. At present, students are charged a rate of interest of 5% p.a. on secured
general loans, 8% p.a. on unsecured general loans and 9% on car loans. The branch has a policy such that
no more than 10% of the total budget should go to unsecured loans and no more than 25% to the car
loans, whilst at least 60% should be general loans of either type. The branch also has a policy that funds
which are not loaned out can be invested in the short-term money market and currently attract a rate of
interest of 7.5% p.a. However, the amount invested in this way at any one time must not be more than
20% of the total.
(a) Formulate the problem of maximizing the monetary return as a linear program.
(b) Suppose now that, the bank is keen to ensure its loan structure is not unduly risky. Each of the four
possible uses of funds has been allocated a risk value by branch manager: 1, 4, 3, 1 respectively for
secured, unsecured, car loans and money market investment. A higher figure indicates a greater risk
in terms of defaulting. The branch wishes to ensure that, on average, the risk factor for the whole
